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The Orthocenter of a Triangle

The Orthocenter of a Triangle
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2020-11-12 21:50
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the orthocenter of a triangle, which is the point where the three altitudes of a triangle intersect. Using GeoGebra commands such as Polygon, OrthogonalLine, and Intersect, the orthocenter can be constructed. Suitable for middle school and above students to learn triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(B, b) → e
  4. OrthogonalLine(C, c) → f
  5. Intersect(f, e) → D
  6. Intersect(e, b) → E
  7. Intersect(f, c) → F
  8. Intersect(d, a) → G
  9. Angle(A, E, D) → α
  10. Angle(C, G, D) → β
  11. Angle(B, F, D) → γ

AI Drawing Prompt Reference

Draw a triangle and construct the altitudes from each vertex to the opposite side. The intersection point of the three altitudes is the orthocenter of the triangle. First, draw the triangle, then draw the altitudes from each vertex, and finally find the intersection point of the altitudes to mark the orthocenter.
The prompt above was compiled from the original drawing commands and is for reference only.